# Surface of Revolution

(redirected from*Area of surface of revolution*)

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## surface of revolution

[¦sər·fəs əv ‚rev·ə′lü·shən]*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Surface of Revolution

a surface that can be generated by revolving a plane curve about a straight line, called the axis of the surface of revolution, lying in the plane of the curve. An example of such a surface is the sphere, which may be considered as the surface generated when a semicircle is revolved about its diameter. The curves formed by the intersection of a surface of revolution with planes passing through the axis are called meridians, and the curves of intersection of a surface of revolution with planes perpendicular to the axis are called parallels. If the z-axis of a rectangular system of coordinates *x, y*, and z is directed along the axis of a surface of revolution, then the parametric equations of the surface of revolution can be written

*x = f(u] cos v y = f {u} sin v z = u*

where f(u) is a function that determines the shape of the meridian and *v* is the angle of rotation of the plane of the meridian.